Is not thanking one's family for their services—out of shyness and sufficing with supplicating for them in one's heart—considered a lack of gratitude to Allah, in accordance with the hadith: "Whoever does not thank people has not thanked Allah," or does it fall under the category of supplicating for someone in their absence?

A person's supplication for someone who has done them a favor in secret is not ingratitude, but rather a shortcoming in showing gratitude. The general principle for thanking people is that it should be done openly, and the supplication for the one who has been favored should be heard, so that the desired reward and praise are achieved. Narrations from the Prophet, peace and blessings be upon him, confirm this, among them his saying: "Whoever does you a favor, recompense him. If you do not find anything to recompense him with, then supplicate for him until you see that you have recompensed him." The best forms of gratitude and praise is saying "May Allah reward you with goodness" (Jazakallahu Khairan) because it is a comprehensive supplication for good in this world and the hereafter, and it is more eloquent in praise. Furthermore, it is recommended for a guest to supplicate for the hosts after eating, as the Prophet, peace and blessings be upon him, said: "May the fasting break their fast with you, and may the righteous eat your food, and may the angels descend upon you." As for the shyness that prevents a person from openly expressing gratitude, it can be addressed through legitimate and psychological means.